Ray Optics & EM Wave Optics

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Ray Optics &

EM Wave Optics

3.46 Fall 2008Photonic Materials & Devices

How can we make an object invisible?


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Resources

Fundamentals of Photonics E. A. Saleh and M. C. Teich

Ch. 1, 2, and 5: ray optics and EM wave optics

Appendix B: linear systems and K-K relation Waves and Fields in Optoelectronics

H. A. Haus

Ch. 1 and 2

Transfer matrix calculation code http://scripts.mit.edu/~sunxc/work/sim/rtfit.html


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Models of light

Propagation models

Free space optics

Ray optics:


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Ray optics: a visual tool (


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Reflection & refraction on curved surfaces

Incident and reflection/refraction angles are taken with

respect to the surface normal


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Optical force: radiation pressure

Wave-particle duality of light

Photons have momentum: p = h /

Force needs to be applied to change the propagation

direction of a photon: p = -Ft

Incident ray Reflected ray

Incident ray

Reflected ray

p

F: radiation pressure


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Radiation pressure in science fictions: solar sail

Count Dookus solar sailer:

Star Wars Episode II: Attack

of the Clones


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Particle movement along waveguide

light

S. Gaugiran et al., "Optical manipulation of microparticles and cells on silicon

nitride waveguides," Opt. Express 13, 6956-6963 (2005)

http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-6956


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Optical tweezers & MOEMS

Move particles, live cells, microspheres

More aboutMOEMS (Micro-Opto-Electro-MechanicalSystems):

A. Ashkin et al., Opt. Lett. 11, 288 (1986). M. Eichenfield et al., Nat. Photonics 1, 416 (2007).

M. MacDonald et al., Nature 426, 421 (2003). M. Notomi et al., PRL 97, 023903 (2006).

D. McGloin, Phil. Trans. R. Soc. A 364, 3521 (2006).


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EM wave optics

Maxwell equations

Constitutive relations (linear media)

Wave equations

Boundary conditions

m/s

EED r 0III !! HHB r 0QQQ !! r

c

cn I~0!


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Plane wave solution

Monochromatic plane wave solution

Wave vectork

A measure of spatial periodicity

where

Poynting vector

rn I~)exp()( tirEE [!

)exp( tirkiAE [!

)exp()exp( zikyikxiktiEzyx !

nc

knk !!T2

0

2222

0

22 ||||zyx kkkknk !!

E

B


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Kramers-Kronig (K-K) relation

nr(refractive index) and K (absorption) are

interdepedent !

g

!0

'

'

)'(21)(

T

dK

CPV

c

nr CPV: Cauchy principle value

Absorption peak Variation of refractive index


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Refractive index (real part) enhancement

via quantum coherence High refractive index material is attractive for a number

of applications, e.g. high NA immersion photolithography

Is refractive index enhancement always accompanied by

absorption increase?

Theoretical proposal: M. Scully, Enhancement of index of refraction via quantum

coherence, Phys. Rev Lett. 67, 1855 (1991).

Experimental realization: N. Proite et al., Refractive Index Enhancement with Vanishing

Absorption in an Atomic Vapor (2008). http://arxiv.org/abs/0807.2584v1

(K) (n)


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Transmission through dielectric interfaces

Boundary conditions of fields The conditions have to be satisfied everywhere and at all

times on the boundary

Derivation of Snells law

Phase matching: continuity of

E-field across the boundaries)exp()exp( zikxiktiAE

zx !

)exp()exp()exp( ,22,33,11 xikExikExikE xxx !

|||||| 22

131

kn

nkk !! Usin|| ! kkx

1

2

2

1

sin

sin

n

n!

U

USnells law


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TE/TM wave optical reflection

TE (transverse electric) polarization

Electric field parallel to substrate surface

TM (transverse magnetic) polarization

Magnetic field parallel to substrate surface

low index high index high index low index

TETM

TETM


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Refractive index of gold

n ~ 0.37 @ 1 eV

Experimentalvalue: R > 90%

%21|37.01

37.01| 2 !

!R

Why isthat ???Imaginary part of index n (extinction

coefficient) contributes to reflection

as well!


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Transfer matrix method

n1 n2

d1 d2

n3

d3

ni-1

di-1

ni

diIncident light

Reflected light Refracted light? ?

Interface

E1

E2

E4

E3)()(

4

3

12

2

1

E

ED

E

E!

Transmission matrices

Boundary

conditions


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Transfer matrix method

n1 n2

d1 d2

n3

d3

ni-1

di-1

ni

diIncident light

Reflected light Refracted light? ?

Transfer matrix

)0

()(t

r

iE

ME

E!

Ei is known

Erand Et can be calculated !


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Anti-reflection (AR) coatings

Quarter wave film

Elimination of reflection on surfaces:

Solar cells

Photodetectors

Photolithography

More general treatment:

Hauss Book, Chapter 1


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Optical cloaking for invisibility:

Plasmonics and metamaterials

W. Cai et al., Optical cloaking with meta-

material, Nat. Photonics 1, 224 (2007).

G. Abajo et al., Tunneling mechanism of

light transmission through metallic films,

Phys. Rev. Lett. 95, 067403 (2005).

T. Ebbesen et al., Nature 391, 667 (1998).

G. Gay et al., Phys. Rev. Lett. 96,

213901 (2006).

W. Barnes et al., Phys. Rev. Lett. 92,

107401 (2004).A. Alu & N. Engheta, Phys. Rev. E 72,

016623 (2005).


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Phase vs. group velocity

Carrier: rapidly varying terms

Propagates at vp Envelope: slowly varying envelope -- information

Propagates at vg

Carries information (digital or analog)

Dispersion: distorts the envelope

http://en.wikipedia.org/wiki/Phase_velocity

http://en.wikipedia.org/wiki/Group_velocity


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Ray Optics & EM Wave Optics

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